We find the slope of y=4x+2 by comparing it
to y=mx+b, and noticing that m=4. [we also
notice that b=2 but we won't use that.]

So we use the point-slope formula to find the
equation of the line with that same slope:

y-y1 = m(x-x1)

 y-4 = 4(x-3)
 y-4 = 4x-12
   y = 4x-8

If you compare that to y=mx+b, you find that this one has the 
same slope but a different value of b, a different y-intercept,
where the line crosses the y-axis.

But your problem stated write the equation using function notation. 

So change the y to f(x) and write:

f(x) = 4x-8

Edwin